Simulation of Urban Effects of Cloud Physical Parameters

A. Mary Selvam and A. S. R.Murty

Indian Institute of Tropical Meteorology, Pune 411 008, India

Proc. Int'l. Conf. on Energy Transformations and Interactions with Small and Meso-scale Atmospheric Processes, 2 - 6 March, 1987, Switzerland.

(Retired) email: [email protected]

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A scale invariant, selfsimilar atmospheric eddy continuum exists in the planetary atmospheric boundary layer spanning several orders of magnitude in scales and gives rise to the observed fractal geometry for the global cloud cover pattern. The global weather systems are manifestations of the unified atmospheric eddy continuum with inherent mutual global-local energy exchange and therefore local urban energy/pollution sources have long-range global effects leading to climate change and environmental degradation. It is shown that the observed scale invariant atmospheric eddy continuum originates from the turbulence scale by the universal period doubling route to chaos eddy growth phenomenon in the planetary atmospheric boundary layer. The cloud dynamical, microphysical and electrical parameters are shown to be simple unique functions of turbulence scale energy generation.

1.    Introduction

The weather systems in the downwind of large industrial complexes are known to be affected by the large quantities of waste heat, moisture, particulate matter and gaseous pollutants released into the atmosphere from the stacks of industries ( Mathews et al., 1971 ). Investigations relating to the interactions of several atmospheric processes are important for climate related studies. Recent studies have indicated selfsimilarity in atmospheric processes and its application for physical processes in the prediction of climate ( Mary Selvam, 1986 ). Governing equations for atmospheric dynamics have been derived and it has been shown that the meso-scale cloud clusters ( MCC ) evolve from a semi-permanent hierarchical atmospheric eddy continuum whose energy structure obeys laws analogous to quantum mechanical laws for the subatomic dynamics. There is selfsimilarity in the dynamical properties of turbulent, convective, meso-, synoptic and planetary scales and a red energy cascade takes place from the turbulence to planetary scales ( Mary Selvam et al.,1984a ). Observations of thermodynamic properties in the troposphere and stratosphere and measurements of plasma irregularities in the ionosphere and the magnetosphere indicate the existence of a continuous spectrum of eddies following a power law n-n where n is the frequency and n is the exponent ( Lovejoy and Schertzer, 1986 ). Hence, for the understanding of the physical processes relating to the urban effects on climate related processes, investigations relating to the dynamics of the atmospheric boundary layer, cloud physical aspects and the coupling of the troposphere - stratosphere - ionosphere are important. These aspects are briefly discussed in this paper.

2.0    Cloud Model

In general, convective elements in the atmospheric planetary boundary layer ( PBL ) are frequently organised in bands ( Eymard, 1985 ) indicating the existence of helical vortex roll ( large eddy ) circulations in the PBL . It is not clear how such well-organised long-lived circulations are maintained in the dissipative turbulent environment of the PBL ( Tennekes, 1973 ). In the following model it is shown that, on the contrary, turbulence of surface frictional origin maintains a semi-permanent hierarchical continuum eddy structure in the PBL .
    The mean flow generates turbulent eddies with a net upward motion at the planetary surface by friction caused by natural and man-made topography and vegetation cover. The incessant turbulence scale upward momentum is progressively amplified by decrease of atmospheric density with height coupled with buoyant energy production from microscale - fractional - condensation ( MFC ) by deliquescence on hygroscopic nuclei even in an unsaturated environment ( Pruppacher and Klett, 1978 ).  A large scale upward motion is imparted to the mean flow by the turbulence scale upward momentum flux and gives rise to the generation of large eddies or vortex roll circulations in the PBL . A conceptual model of the large eddies in the PBL is given at Figure 1.


Figure 1 : Eddies in the PBL

    The turbulent edies are carried upward on the envelopes of the large eddies. Buoyant turbulent kinetic energy generation by MFC occurs in the environment of the turbulent eddies and gives rise to the formation of microscale capping inversion ( MCI ) layer on the large eddy envelope. The MCI is seen as the rising inversion of the day time PBL in echosonde and radiosonde records.
    Townsend ( 1956 ) has derived the following relationship between the large and turbulent eddy root mean square ( r. m. s ) circulation speeds and w*  and their respective radii R and r as follows


 W is approximately equal to 0.25 for R/r = 10 where R/r is the length scale ratio z . Therefore upward turbulent vetical velocity production at the planetary surface gives rise to upward propagating large eddies or gravity ( buoyancy ) waves.
    The MCI is a region of vertical mixing since the turbulent eddy fluctuations mix overlying environmental into the large eddy volume. The fractional volume dilution rate k of the total large eddy volume by vetical mixing is derived as ( Mary Selvam et al., 1985a )


where w* is the turbulent vertical velocity production by MFC and dW is the corresponding increase in the large eddy circulation speed. The value of k is greater than 0.5 for length scale ratio z less than 10 . Though a continuous spectrum of eddies propagate outward from the planetary surface , only those eddies with length scale ratio greater than or equal to 10 can exist as discrete, identifiable, semipermanent entities in the PBL  since dilution by vertical mixing erases their ( large eddy ) signature for smaller scale ratios. In summary, the PBL contains a semipermanent hierarchical system of eddies consisting of the convective, meso-, synoptic and planetary scales which evolve basically from the dominant turbulence scale at successive decadic scale range intervals and is manifested as mesoscale cloud clusters and cloud rows in global synoptic weather systems. Enhanced condensation inside clouds amplifies the myriads of turbulent eddies and gives rise to cloud top gravity oscillations. Cloud water condensation in the innumerable turbulent eddies is responsible for the observed cauliflower-like surface granularity of the cumulus cloud. The physical mechanism of growth of the atmospheric buoyancy ( gravity ) waves from turbulent buoyant energy production is analogous to the conditional instability of the second kind ( CISK ) mechanism ( Holton, 1979 ) where hurricane systems are postulated to derive their energy from convective scale cloud condensation. Also there is an inherent two-way energy feedback mechanism in the hierarchical system of eddies discussed in this paper and given in Equation 1 which is a statement of the law of conservation of energy, selfsimilarity and self-consistency in atmospheric processes. The kinetic energy E of unit volume of the atmospheric eddy of frequency n may be shown to be equal to Hn where H is the instantaneous spin angular momentum of unit volume of planetary scale eddy about the earth's axis. It is further shown ( Mary Selvam, 1986 ) that the eddy energy spectrum gives the probability density distribution of the eddy field. Thus, the physical laws governing eddy dynamics in the macroscopic planetay atmosphere is analogous to the quantum mechanical laws of the sub-atomic space. Therefore the mesoscale cloud clusters are a visible macroscale manifestation of the universal quantum mechanical nature of the energy stucture of natural phenomena. The full continuum of atmospheric eddies exist as a unified whole in time and space and contribute to the manifested atmospheric phenomena in the global planetary atmosphere and such a concept is similar to the bootstrap theory of Chew ( 1968 ) and the theory of implicate order envisaged by Bohm ( 1951 ).
    The relationship between the size ( R ) , time period ( T ), circulation velocity ( W ) and energy ( E ) scales of the convective ( c ) , meso- ( m ), synoptic ( s ) and planetary ( p ) scale atmospheric eddy system to the basic turbulence scale ( t ) is derived from Equation 1 and is given below.

R : Rt = r : 10r : 10 2r : 10 3r : 10 4r
T : tt = t : 40t : 40 2t : 40 3t : 40 4t
W : Wt = w* : 0.25w* : 0.25 2w* : 0.25 3w* : 0.25 4w*
E : Et = e : 62.5 e : 62.5 2e : 62.5 3e : 62.5 4e


    The globally observed quasi-biennial oscillation ( QBO ) and the 20-year cycle in weather patterns ( Burroughs, 1986 ) may possibly result respectively from the fundamental semi-diurnal atmospheric oscillation ( QBO ~ 12 hrs x 402 ) and the 5 - minutes oscillations of the sun's atmosphere ( 20 years ~ 5 minutes x 404 ) ( Equation 3 ). Such a process is analogous to anti-Stokes laser emission triggered by laser pump.

2.1    Wind Profile in the PBL

The large eddy growth occurs in the vertical across unit cross-section of the large eddy envelope in length steps dR equal to the turbulent eddy radius r since it is during this upward turbulent displacement of air parcels in the MCI that a large eddy circulation velocity increase dW per second occurs because of turbulent buoyant energy production by MFC . The circulation velocity  W of a large eddy of radius R which begins growth from turbulence scale r from the planetary surface is therefore obtained from Equation 2 as

k = 0.4 for z = 10

    This is the well known logarithmic wind profile relationship in the surface ABL and the Von Karman's constant k is now defined by the new theory as representing the fractional volume dilution rate of the large eddy by vertical mixing due to turbulent eddy fluctuations for a scale ratio of 10 . Further, the theory states that the logarithmic wind profile relationship prevails throughout the PBL , the absolute value of W being determined solely by MFC in the dominant turbulent eddy. Logarithmic spiral airflow tracks ( vortices ) are therefore associated with vortex roll circulations and is consistent with observations ( Hauf, 1985 ). The atmospheric eddy continuum therefore consists of a hierarchical system of vortices within vortices.
    The parcels of air rising up from the surface in the updraft regions of large eddy circulations get diluted by vertical mixing and only a fraction f reaches the normalised height z and is given by ( Mary Selvam et al ., 1985 ).


W = w* f z


    Since the eddy energy is derived from microscale fractional condensation on hygroscopic nuclei in the troposphere the eddy enegy spectrum is dependent on the atmospheric nuclei size spectrum. The observed atmospheric nuclei spectra follow the Junge aerosol size spectrum ( Pruppacher and Klett, 1978 ) and it is shown that the observed aerosol size spectrum is a natural consequence of the atmospheric eddy continuum ( Ramachandra Murty et al ., 1985 ). The aerosol size spectrum has a computed maximum spectral slope of -4.8 in the maximum size region.

2.2    Atmospheric Eddy Energy Spectrum

The atmospheric eddy energy spectra obtained by observations of turbulence spectra of wind in the PBL show the existence of a continuous spectrum of eddies with universal characteristics of scale invariant spectral slope ( Nastrom and Gage, 1985 ).
    The atmospheric eddy energy spectral slopes Sd and Sm corresponding respectively to dry and moist atmosphere are computed ( Ramachandra Murty et al ., 1985 ) and shown to agree with observations.
    Selfsimilarity and scale invariance are implied in atmospheric processes since the eddy energy spectrum follows a power law of the form  n-n where n is the frequency and n is the exponent. It is therefore theoretically possible to predict weather trends and physical/chemical characteristics of air motions at all scales provided  n is known.

2.3    Synoptic Scale Cloud Bands

The cloud bands identify the circulation path of the synoptic eddy whose radial growth occurs in legth steps dR equal to r and the corresponding angular rotation dq may be shown to be equal to f . Therefore in regions of weak pressure gradients, r is large and dq small and cloud rows occur. With increasing moisture supply, r decreases and dq increases resulting in tight coiling of cloud bands as in hurricane systems ( Mary Selvam, 1986 ).
    The pressure and wind anomaly patterns of synoptic eddy systems are universal with respect to the normalised length scale and are shown at Figure 2.

Figure 2 : Universal pressure and wind anomaly patterns in synoptic eddy systems

Decrease in r results in increase in absolute values of the pressure and wind gradients.
    The above physical mechanism envisaged for atmospheric eddy growth postulates the co-existence of large and small eddies in a hierarchical system with ordered dynamical local-global mutual energy exchange and therefore all energy systems are inherently non-local. It is shown that such a concept leads to the universally observed normal distribution characteristics in natural phenomena. Also, Lovejoy and Schertzer( 1986 ) have established the fractal characteristics of rain areas and rainfall in association with the observed scale invariant characteristics of the atmospheric eddy energy spectrum. The regions of eddy continuum energy enhancement are conventionally associated with ordered chaos. The universal route to chaos, namely, period doubling, intermittency and scale invariant eddy energy structure ( Harrison and Biswas, 1986 ) is commonly observed in all natural growth phenomena ( Fairbairn , 1986 ) and therefore is an inherent characteristic of the quantum mechanical nature for the eddy energy structure manifestation in natural phenomena. Since eddy circulation inherently consists of opposite directions of motion in association with different manifested phenomena, the apparent quantisation of energy in nature occurs. Eddy motions or vibrations in the PBL are responsible for the observed normal distribution characteristics of thermodynamical parameters as explained in the following. The eddy energy propagates by the inherent property of inertia of the medium and therefore w* , w*2 , w*3  and w*4  respectively represent the inertia, force, angular momentum and spin angular momentum of the medium caused by the eddy motion initiated by the turbulence scale acceleration w* per second. Therefore, the mean ( w ), variance ( s2 ), skewness and kurtosis are respectively given by w* , w*2 , w*3  and w*4 . The moment coefficient of skewness is equal to zero. The moment coefficient of kurtosis is equal to three and represents a factor of three increase in the spin angular momentum for the inherent period doubling process of large eddy growth in the MCI . Therefore the normal distribution characteristics conventionally attributed to random chance are in reality the deterministic laws of eddy growth by the period doubling process and represent the implicit order in natural phenomena. Signal and noise exist in each other in nature since signal is but the integrated mean of the conventional background random noise over large space and time scales. Further, the following fundamental relations in statistics and mathematics may be obtained from the physical concept of the eddy growth mechanism as follows. The standard equation relatining population and sample standard deviation follows from Equation 1, namely, W22 = W12 /n where n = z2 / z1 , and z1, z2 are the respective scale ratios with respect to the turbulence scale for two large eddy circulations of root mean square circulation speeds W1 and  W respectively. The function f also gives the angular displacement of the particle trajectory on the large eddy envelope for successive radial growth steps r and it may be shown that f = p = 22/7 = circumference/diameter  for a complete large eddy circulation of scale ratio 10 . The hierarchical growth of large eddies from turbulence scale is basically by a period doubling process in the MCI  where incremental growth occurs in length steps equal to r . The layer MCI is thus a region of chaos. The unique particle trajectory design of concentric circles in the field of chaos has been named the strange attractor and results from the inherent hierarchy of the continuum vortex roll circulations. For example, the strange attractor design is seen in the MCI where maximum aerosol concentration occurs with a layered fine structure representing the component turbulent eddies and has been observed commonly in the stratospheric Junge aerosol layer, the arctic haze ( Radke et al ., 1984 ) and more spectacularly in the planetary rings of Jupiter, Saturn and Uranus ( Michel, 1985 ) indicating dusty debris filled atmosphere and violent equatorial convective dynamics for the major planets. Particles in the planetary rings may be shown to follow the relation R3 / T2 = constant from Equations 1 and 2 and is therefore consistent with Kepler's third law of planetary motion.

2.4    Cloud Microphysics and Dynamics

Cloud growth occurs in the updraft regions of vortex roll circulations in the low pressure field of synoptic scale systems. From the theory of of atmospheric eddy dynamics it is shown that (1) The vertical profile of the ratio of q , the actual cloud water content to the adiabatic liquid water content qa follows the f distribution. (2) The vertical  profiles of the vertical velocity W and the total water content qt are respectively given by W = w* fz and qt = q* fz where t represents the total values and   *  represents cloud base values. (3) The cloud growth time T = [ li {sqrt(z)}]2z  where  li  is the logarithm integral. (4) The cloud drop size spectrum follows the Junge aerosol size spectrum and (5) The computed raindrop size spectrum closely resembles the observed Marshal-Palmer raindrop size distribution at the surface ( Mary Selvam et al ., 1985).

3.0    Planetary Atmospheric Electrification

3.1    Fair Weather Electric Field

The atmospheric eddy continuum circulations give rise to vertical mass exchange in the ABL such that a net positive space charge current flows upward with a simultaneous downward transport of negative space charges from ionospheric levels and this dynamical two-way charge transport is shown to be of the right order of magnitude and direction to sustain the fair weather atmospheric electric field and also explain the horizontal component of the geomagnetic field distribution ( Mary Selvam et al ., 1984b ). The above theory also helps to explain the observed ( Gribbins, 1981 ) close similarity between the geomagnetic field lines and atmospheric circulation patterns. Therefore, changes in atmospheric circulation patterns preceding climate changes can be detected in geomagnetic field pattern variations. The wandering of the geomagnetic north pole is therefore closely related to global climate variations and incidentally is also reflected in the subatomic dynamics of ferromagnetic substances which naturally align themselves along geomagnetic N-S direction.

3.2    Cloud Electrification

It is shown that cloud top gravity oscillation mix overlying environmental air into the cloud such that there is a downward transport of negative space charges from above cloud top regions and a simultaneous upward transport of positive space charges from below cloud base levels to the cloud top regions. Positive dipole cloud charging occurs by the vertical mixing. The electric field at the surface due to the cloud dipole charge, the strength of the cloud dipole, the cloud electrical conductivity, the corona discharge current are expressed in terms of the basic non-dimensional parameters f and z ( Mary Selvam et al ., 1984b ).

4.0    Cloud Dynamics and Urban Effects

The thermal energy input from industrial/urban sites in combination with hygroscopic nuclei and moisture lead to enhanced cloud growth process with taller clouds and heavier rainfalls particularly in the downwind region. A fraction f of the surface nuclei form cloud/raindrops and therefore the same fraction f of atmospheric pollution content will also get washed down in the rain. Even in clear weather conditions the pollution of atmospheric air in the form of aerosols will be equal to a fraction f of the value at the source location. The steady state flux of pollution transport can therefore be taken to be given by the f distribution both in the vertical and horizontal. Though f is small at large values of the normalised distance z , yet long-term accumulations of pollution will be appreciable resulting in irreversible environmental degradation. Also, enhanced dynamics associated with thermal energy supply from the urban industrial sites leads to a faster transport of pollutants in all directions.
    One possible solution to prevent soil and rain water acidification is to release alkaline mineral dust ( natural soil ) along with the chimney gaseous effluents since cloud drops form on large aerosols and therefore rainwater acidificaion may be prevented. Such instances of inadvertent neutralisation of acid rain in the meditteranean/ European countries has been observed in association with Saharan dust episode resulting from the African drought and the El-Nino ( Loye-Pilot et al ., 1986 ). Also, Indian region rainfall even in close vicinities of industies is found to have alkaline rain in association with the alkaline nature of the dust content in the air ( Khemani et al ., 1985 ).

5.0    Atmospheric Vortices and Stratospheric Dynamics

Thermal energy sources are regions of enhanced eddy dynamics and vertical mixing extending to the stratosphere and above. Enhanced downward flux of stratospheric ozone occurs above regions of industrial/urban activity. Beig and Chakravorthy ( 1986 ) have reported a sharp decrease in stratospheric ozone in association with a major fire in an off-shore oil well in India. Downward transport of stratospheric ozone occurs in regions of deep convection ( Gushchin and Sokolenko, 1985 ) . Stratospheric aerosol and radioactive debris from volcanic eruption and nuclear experiments/accidents are transported downwards to surface levels in regions of deep convection where intense vertical mixing occurs. Such regions of stratospheric contamination deposition on surface even in fair weather will occur in discrete areas of fractal nature analogous to rainfall areas ( Lovejoy and Schertzer, 1986 ) and thus may account for the radiation hot spot fall out pattern reported following the Chernobyl nuclear reactor accident ( Nature, 1986 ). Also, the recently reported ozone hole in the Antarctic stratosphere ( Tung et al ., 1986 ) may possibly be caused by the increased international exploration activities in Antarctica during the spring/summer season in recent years.

5.1    Atmospheric Vortices and Ionospheric Dynamics

It is known that solar flares perturb the ionosphere and cause intensification of weather systems. Therefore ionospheric heating experiments and the numerous earth orbiting satellites may possibly create fine scale magnetospheric/ionospheric perturbations and lead to inadvertent modification of climate, for example, the African drought, anomalous El-Nino and abnormal hurricane activity.

6.0    Conclusions

Energy structure of natural phenomena in the PBL are inherently scale invariant with a two-way energy feedback mechanism between the larger and smaller scales. Persistent local microscale modifications of the atmospheric composition and energy structure is bound to be manifested in course of time in a magnified version in the macroscale as global changes in atmospheric composition, climate and dynamics. Urban/industrial activities are therefore unavoidably linked with global climate change and environmental pollution, the latter of which can possibly be averted by suitable preventive measures.


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